Regularity for Eigenfunctions of Schrodinger Operators

被引：14

作者：

Ammann, Bernd ^{[1
]}

Carvalho, Catarina ^{[2
]}

Nistor, Victor ^{[3
]}

机构：

[1] Univ Regensburg, Fak Math, D-93040 Regensburg, Germany

[2] Univ Tecn Lisboa, Inst Super Tecn, Dept Math, P-1049001 Lisbon, Portugal

[3] Penn State Univ, Dept Math, University Pk, PA 16802 USA

来源：

LETTERS IN MATHEMATICAL PHYSICS | 2012年 / 101卷 / 01期

基金：

美国国家科学基金会;

关键词：

Hamiltonian; Schrodinger operator; eigenvalues; bound states; regularity of eigenfunctions; blow-up of singularites; singular potentials; multi-electron atoms; DIFFERENTIAL-OPERATORS; ASYMPTOTIC-BEHAVIOR; SOBOLEV SPACES; MANIFOLDS; APPROXIMATION; EQUATION; SYSTEMS; DECAY;

D O I：

10.1007/s11005-012-0551-z

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We prove a regularity result in weighted Sobolev (or Babuka-Kondratiev) spaces for the eigenfunctions of certain Schrodinger-type operators. Our results apply, in particular, to a non-relativistic Schrodinger operator of an N-electron atom in the fixed nucleus approximation. More precisely, let be the weighted Sobolev space obtained by blowing up the set of singular points of the potential , , . If satisfies in distribution sense, then for all and all a a parts per thousand currency sign 0. Our result extends to the case when b (j) and c (ij) are suitable bounded functions on the blown-up space. In the single-electron, multi-nuclei case, we obtain the same result for all a < 3/2.

引用

页码：49 / 84

页数：36

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[2]

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